rpc - lecture 5

8/12/2019 RPC - Lecture 5

1/10

iutirugffi*tfrReinforced and Prestressed Concrete -Cs-Wf,ffi;Hkfrf'##

uttfl*qwr)

2)

3)

Rectansular Seclion with Compression Reinforcement{Double Rcinforced Rectangular Beams)

to revcrsal monrent for ihe beams ofa rcinforecd frame (thrtension reinforcement provided for the negafive monenfbrcomes the compression steel under positive nomnt).to incre*se lhe n$ment resisting capacity oftke secti,on {when isnot possible to change the dimensions of the heam).to reduce the loag-term deflectioa of au element under serviceI*ads {when the conf,rete begius fo creep, the compressivc forcein the beam is tralsferred frnu the concrete fn the steel thusthe cnncrete stress is lowered and de{leetioa due to creep ismuch reduced),

...>. ..-* *- r".


2/10

wfiffiA. Ilesietr of rectanqular reinforced concrete scction with compression reinforcement

I M-.,f&" " .';* 'o': i" - -b:41 :{*d - ){re d*{$r dtir;rate uanrmt sxced-r llrsfio*s* tlf Gi*tfle af tkc crmete ardcanpres-


3/10

B. Analvsis of doublv reinforeed rectansular section. the resistance moment of the section:

' the reinforeemeDts sfrsins:&* =e,::- e." =i.5*l *JJ

z -d,{',,. =a--

r:, = lffiiffiV,/-r ' '/w. the steel in tension and the steel in conprcssion yields if:

andffi

nf.u. EJ.- -r:' .h,il {:':frr

ffi5ffi

r if the steel uot yields, then the steel is in the elartic domrin and the strsse$ are:

rr -aad" =rq;-t -------------> forttrsion

-;for compression*r =s*:s, "4,-*]

pggggpf: find the restutancc moment xten tte tension stell yields rnd the comprrssion stelie in the elsrtic domdn: nlf '.4 '--' o.:-3'lo'tif s"


4/10

"=xo-f x-fJ= r?'@ r'csa t--@x/" Z-8*'\r=rsr*.,u='.*-; ccd* 1'='rut'/-' I l|' 1l-- *?r,lml tl n -4E6"=(i._-uoI:r=(ror-rs?E{=+s.c.* I ll rWo.E.e.,/ 0.r.r50-t1.tt J_lq *6.,{8 m:

odly tensio reinfsfcqentitIxa $lc l-Ietue4)

Ifo eryi.&.*.f .tud-* 2

r=j=ffi=o,rn < ek -(?4,= 3- = '5,95 = tt . m - = t.T -------) the wmpmioo,$cel= d j Jo ' M- ," - is in the elastic doBaitr (mt yields)

=aJ'4*J?'r5s.l]J{ri? -s.4.{cJtl+ rfi .r4{rlr-ro}= l3,r?.r0"r.id * 3j'?&ns

Examrle 3: sing\rversus doubtereirforced sections

lg- =333?&tl.ldodi. ftiibrdd L=@stogly reirhrEd,r=rso-{u"tf J=zro*r=1,g; Js'l& -q5*:r*e=j=ff=r.a


5/10

Efaurnle 4: if we doubl,e lhe reinforcing pcrcentage of the resistance rteel both in the case ofend doubly rellforeed sections, we obtrir:, - {4' :_,r"_lro = H:_39lFg9 _,***ti.n^h f- n,$ l5ll. -$t;=j=ffi=csr:. e-=ar

.'=._=4{-3-3,-a[_-r,rs d, B 1Q-L"l'**r***r*" Il-umpr*rrmrmJt*., - u***;[, -*] * a"r"da -a. ]n* ={* r{*,r* r$dH$-iii 8r.l8si}dd1-il$r$,

l.rf* =5tJ6'#A

J " =r*ttw:4,=]15m4 * le*d =]lt"5ar

ci&sly

rKtfficirgFConclusions:o in normal reinforcing ritaations, the compression reinforcement not leads to a significant increaseof tte resistence cep*city,o tc over-reitforced elemrlts, the comFrerrion reinforcement lerde to a signifcant increaseof th resistascc capacityo' it is nol economic to use compression reinforcemnt in a sectlon before atl the singly reinforcingpossibiliticr are used

l-tll tr" t-* n-al '{.{t.qlts*r . re * 4 3


6/10


7/10


8/10

FlanaeS Section - the Peoth of the Strsp Bloek Exbn{s Eplorr,the FIarFp

Efr

'.,|ilrarilllnIlesisn lglalion$;

t ' u l' ft, -**.4,t 'dM rr - Mu.r+ frfu., + N o,4r= 4u+ 1,., + 1.,z. =d-O5fu z"z=d _frSht z"t=d -d:lf *, = Fo "4$*ixrdf,ta'0.:,tri#s"r = qf*r6 *l-hA{a -qsA, }M n: * 4'f,8,., = 4,fd{d *41ffsr = I{*r - H u: = Iru-& -4tfd.{d-Lnr. } - Is"rTr," -t,-{}t*-'1,-*}}f* : ff*-*44tf. ,'jtf^


9/10

::l; . ffi,',,t,ttf, i:lrtc

&{or*po;parl2fnif-: * $r - qlrff.(a -o.u*, lifrd,, *Xter *Itt*d, *#x.,,*,zfrqa *drl=i8r-e6l'l*-{6^&-Frsf*{d*gs4l I #,

-o,$,r-*_l?[fr.,1,-4d *t,: {* n",f,t- i'* s 4u*4:


10/10

wfiq&ryf v,o hr i b ,i , kr',1r,-l o" n.r.l ll.ll i i.-r ll"'Ln*.a:.t* ,f .&* ll ,t'l

fpi-*".',-&r.U.n..,.L '1 t.r.rl =[**.4.;.;1,-* i** *. i.ry].q.ft( ; iIt-t4a'4 -i'l , -to l{n *rir-d{.11' .tl

ttfqalf. Eg f 5rffi: lf& Ji;f&I$&*r4LtE' 'fr-t &."dqfa.**b;t =&.

d-. /*l a,\,+_ I4:4t1- lJtbir',Id i. rl rl

*='-"*l*-ili,-,.*i

itr=1-$::;;*=i* {'-?f3]"'ff4o-$b.i a.ib+t;-r*t*h,ff uan

rpc - lecture 5

Documents